S Rank
Aegislash 
Aegislash is particularly dangerous due to King's Shield messing with physical attackers, and his ability to run either Special, or physical attack sets.
An Offensive Counter that works well is Bisharp. With Defiant the attack drop from King's Shield is negated, and his Dark type stabs can easily kill, or seriously maim Aegislash. He also resists Shadow Sneak, meaning that Aegislash is forced to move after to use a more powerful move. Another potential physical counter is Infernape who can utilize Overheat or Flare Blitz.
A Defensive counter is difficult due to Aegislash's ability to run such diverse sets. I've found that Umbreon can stall both Aegislash sets well. Sacred Sword is a potential threat, but a Defensively oriented Umbreon set should be able to handle it well enough.
Charizard Mega-Y 
Charizard Mega-Y is a particularly threat due to his Sun setting ability and access to Solarbeam. Any Scarfer with a Rock move can handle him, but another option is EBelt Noivern who can Outspeed and kill Charizard-Y with Hidden Power Rock. Defensively, you could use a fire type who can tank Fire Blast or Solarbeam, but will tend to get hit by Focus Blast. Chandelure could potentially handle the classic Fire Blast, Solarbeam, FBlast and Roost set.
Charizard Mega-X 
Charizard Mega-X has a wicked attack stat and access to Dragon Dance. One Pokemon who could be used to deal with him is Hippowdon who has incredible Defense and HP, a STAB Earthquake and access to Slack Off, a reliable recovery move. Offensively you could use Band Terrakion who can outspeed with 252 Speed EVs. Jolly can be used, but Band Adamant is scary.
Mega Pinsir 
Speed + Attack + Swords Dance = death and destruction.
Rotom-Wash has been used as a Defensive counter and it's.... ok
+2 252 Atk Aerilate Mega Pinsir Return vs. 252 HP / 252+ Def Rotom-W: 169-200 (55.5 - 65.7%) -- guaranteed 2HKO after Leftovers recovery
It cannot safely switch into +2 Pinsir. Someone who can is Skarmory with 252 HP / 244 Def who then takes less than 50% damage from +2 Return.
Offensively your best bet is to use Talonflame who has access to priority Brave Bird and can move before Quick Attack.
Thundurus-I 
Thundurus is not quite on the level of offense that it's Therian counterpart is, but it does have access to Prankster which makes it dangerous. The Pokemon with coverage moves like Terrakion are crippled by TWave, and you can't stall it due to Taunt. One of the options you have is to use a ground type, but they tend to fall to HP Ice. Dugtrio can outspeed, but it can't KO. One of your options here is to use Guts Conkeldurr who doesn't care about Taunt, can easily tank special attacks with an Assault Vest, doesn't really care about the Paralysis Speed Drop, and can easily KO Thundurus with Ice Punch.
A Rank
Bisharp 
An Easy way to counter this guy is by using Conkeldurr or Breloom who both have access to Mach Punch and don't really care about Sucker Punch. Another option would be one of the Justice Trio (Terrakion, Virizion, Cobalion) who get an attack boost from dark moves with Justified, and can outspeed Bisharp otherwise. Defensively, you can use Rotom-Heat who can speedcreep, and has access to Will-O-Wisp making him unaffected by Sucker Punch, and safe from other phsyical attacks thanks to the burn.
Deoxys-D 
Deoxys-S 
I'm doing these two together because they're counters are largely similar. Both of them get hurt by Prankster Taunt which you can use Sableye or Thundurus-I for. Deo-S isn't a majorly offensive threat, so a good option is often Scizor you can Bug Bite and then Bullet Punch, same for Deo-D, who's HP leaves it vulnerable to attack. Then you simply bring in your SPinner or Defogger and remove the hazards.
Garchomp / Mega Garchomp 
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These two have a good weakness you can target, their speed. They are outsped and can be easily dealt with by opposing dragon types, or those with HP Ice. Otherwise a good option is Mamoswine who can either tank their hits, or strike with Ice Shard. Defensively a Physical wall would be nice, Skarmory and Ferrothorn come to mind, but if Garchomp utilizes Fire Fang then Ferro will bite the dust.
Heatran 
Ground Move. GG.
But seriously, Heatran is able to run a large variety in sets thanks to his diverse stats and movepool. Florges/Sylveon can both handle his offensive sets fairly well, except Specs, but that's used far less than the AV Heatran.
252+ SpA Heatran Flash Cannon vs. 252 HP / 252+ SpD Sylveon: 174-206 (44.1 - 52.2%) -- guaranteed 3HKO after Leftovers recovery
His Defensive set is often ruined by water types due to his only offensive moves being Lava Plume and Earth Power. Another option is Air Balloon Heatran who is immune to both those moves, but that's largely situational.
Kyurem-B 
Such Attack, much speed ;-;
Scizor Bullet Punch, eat this have fun gg.
Defensively Hippowdon is a good option, or you can use Klefki to set up screens then bring someone in. Kyurem-B is not hard to predict as his usable moves are fairly obvious, Fusion Bolt, Ice Beam, Dragon Claw, Outrage and Substitute are common. His most common item would be Scarf iirc.
But yeah, use Scizor, wreck him.
Landorus-I 
Landorus-T 
Fairly similar so same answer for both.
Landorus is a threat due to his speed, his access to U-Turn, and of course, his movesets (Special for Incarnate, physical for Therian) . A good option for walling Lando would be Rotom-Wash (Who can just kill him with Hydro Pump) or Mandibuzz who can handle him with it's Special Defense spread. Offensively use Mamoswine Ice Shard or anything faster with Ice Beam/HP Ice.
Manaphy 
Manaphy can easily be handled by Mega Venusaur, or Rotom-Wash who both resist it's moves, and can deal hefty damage with their respective STABs. Not much to say past that, don't let it set up.
Continued in second answer (character limit)
Pictures taken from Smogon, all words written from my own head, calcs down using the PS Calculator.
